June 1 (Reuters) - U.S. stocks were higher on Thursday after better-than-expected private sector hiring showed that the labor market continues to strengthen, further boosting chances of a rate hike by the Federal Reserve later this month.

ADP also revised higher its count of new small business jobs for the previous two months, now reporting a 126,000 gain in March and 68,000 new jobs in April.

Employment in the USA private sector increased by much more than anticipated in the month of May, according to a report released by payroll processor ADP on Thursday.

James Chen, head of reasearch, at Forex.com in Bedminster, New Jersey said he expects a strong jobs report on Friday that would reinforce a Fed rate hike this month.

Employment is expected to increase by 185,000 jobs in May after jumping by 211,000 jobs in April.

Despite the monthly decrease, the report said total construction spending was up by 6.7% compared to the same month a year ago.

Traders now anticipate a 94.7 percent chance the Fed will raise rates by a quarter point at its June 13-14 meeting, according to Thomson Reuters data. S&P 500 e-minis were up 3 points, or 0.12 percent, with 120,697 contracts traded.

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The MSCI world equity index, which tracks shares in 45 nations, rose 1.56 points or 0.34 percent, to 465.35.

That, however, was offset by a fairly positive USA manufacturing report from the Institute for Supply Management, which showed its index edging up to 54.9 with gains in the employment and new orders components. The data is expected at 10:00 ET.

"While the claims report put a damper on what has been a pretty upbeat run for most of the recent labor market data, we still have a fairly favorable view of labor market conditions", said Daniel Silver, an economist at JPMorgan in NY. "I think we are looking at another trying session", Cardillo said. A broader measure of unemployment, which counts unemployed people, discouraged workers and those working part-time who can't find full-time work, also dropped to a almost 10-year low, at 8.6 percent.

Prior to the ADP release, analysts were forecasting a gain of 172,000 in the private employment component of the official data.

Goodyear Tire's shares were up 5.7 percent at $34.03 after Morgan Stanley raised its rating to "overweight" from "underweight".

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